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(k,n)-threshold secret image sharing (SIS) protects an image by dividing it into n shadow images. The secret image will be recovered as we gather k or more shadow images. In complex networks, the security, robustness and efficiency of protecting images draws more and more attention. Thus, we realize multiple secret images sharing (MSIS) by information hiding in the sharing domain (IHSD) and propose a novel and general (n,n)-threshold IHSD-MSIS scheme (IHSD-MSISS), which can share and recover two secret images simultaneously. The proposed scheme spends less cost on managing and identifying shadow images, and improves the ability to prevent malicious tampering. Moreover, it is a novel approach to transmit important images with strong associations. The superiority of (n,n)-threshold IHSD-MSISS is in fusing the sharing phases of two secret images by controlling randomness of SIS. We present a general construction model and algorithms of the proposed scheme. Sufficient theoretical analyses, experiments and comparisons show the effectiveness of the proposed scheme.

We consider the Beurling zeta function ζP(s), s=σ+it, of the system of generalized prime numbers P with generalized integers m satisfying the condition ∑m⩽x1=ax+O(xδ), a>0, 0⩽δ<1, and suppose that ζP(s) has a bounded mean square for σ>σP with some σP<1. Then, we prove that, for every h>0, there exists a closed non-empty set of analytic functions that are approximated by discrete shifts ζP(s+ilh). This set shifts has a positive density. For the proof, a weak convergence of probability measures in the space of analytic functions is applied.

We study properties of eigenvalues of a matrix associated with a randomly chosen partial automorphism of a regular rooted tree. We show that asymptotically, as the level number goes to infinity, the fraction of non-zero eigenvalues converges to zero in probability.

For a sequence Xn,n⩾1 of independent random elements taking values in a Rademacher type p Banach space with the k-th partial sum Sk(k⩾1) , we provide necessary and sufficient conditions for the convergence of ∑n=1∞1nP(max1⩽k⩽n‖Sk‖>εnα) and ∑n=1∞lognnP(max1⩽k⩽n‖Sk‖>εnα) for every ε>0 .

Random finite element method (RFEM) provides a rigorous tool to incorporate spatial variability of soil properties into reliability analysis and risk assessment of slope stability. However, it suffers from a common criticism of requiring extensive computational efforts and a lack of efficiency, particularly at small probability levels (e.g., slope failure probability P f  < 0.001). To address this problem, this study integrates RFEM with an advanced Monte Carlo Simulation (MCS) method called “Subset Simulation (SS)” to develop an efficient RFEM (i.e., SS-based RFEM) for reliability analysis and risk assessment of soil slopes. The proposed SS-based RFEM expresses the overall risk of slope failure as a weighed aggregation of slope failure risk at different probability levels and quantifies the relative contributions of slope failure risk at different probability levels to the overall risk of slope failure. Equations are derived for integrating SS with RFEM to evaluate the probability ( P f ) and risk ( R ) of slope failure. These equations are illustrated using a soil slope example. It is shown that the P f and R are evaluated properly using the proposed approach. Compared with the original RFEM with direct MCS, the SS-based RFEM improves, significantly, the computational efficiency of evaluating P f and R . This enhances the applications of RFEM in the reliability analysis and risk assessment of slope stability. With the aid of improved computational efficiency, a sensitivity study is also performed to explore effects of vertical spatial variability of soil properties on R . It is found that the vertical spatial variability affects the slope failure risk significantly.

Secret image sharing (SIS), as one of the applications of information theory in information security protection, has been widely used in many areas, such as blockchain, identity authentication and distributed cloud storage. In traditional secret image sharing schemes, noise-like shadows introduce difficulties into shadow management and increase the risk of attacks. Meaningful secret image sharing is thus proposed to solve these problems. Previous meaningful SIS schemes have employed steganography to hide shares into cover images, and their covers are always binary images. These schemes usually include pixel expansion and low visual quality shadows. To improve the shadow quality, we design a meaningful secret image sharing scheme with saliency detection. Saliency detection is used to determine the salient regions of cover images. In our proposed scheme, we improve the quality of salient regions that are sensitive to the human vision system. In this way, we obtain meaningful shadows with better visual quality. Experiment results and comparisons demonstrate the effectiveness of our proposed scheme.

Let P be the set of generalized prime numbers, and ζP(s), s=σ+it, denote the Beurling zeta-function associated with P. In the paper, we consider the approximation of analytic functions by using shifts ζP(s+iτ), τ∈R. We assume the classical axioms for the number of generalized integers and the mean of the generalized von Mangoldt function, the linear independence of the set logp:p∈P, and the existence of a bounded mean square for ζP(s). Under the above hypotheses, we obtain the universality of the function ζP(s). This means that the set of shifts ζP(s+iτ) approximating a given analytic function defined on a certain strip σ^<σ<1 has a positive lower density. This result opens a new chapter in the theory of Beurling zeta functions. Moreover, it supports the Linnik–Ibragimov conjecture on the universality of Dirichlet series. For the proof, a probabilistic approach is applied.

We propose novel goodness-of-fit tests for the Weibull distribution with unknown parameters. These tests are based on an alternative characterizing representation of the Laplace transform related to the density approach in the context of Stein’s method. Asymptotic theory of the tests is derived, including the limit null distribution, the behaviour under contiguous alternatives, the validity of the parametric bootstrap procedure, and consistency of the tests against a large class of alternatives. A Monte Carlo simulation study shows the competitiveness of the new procedure. Finally, the procedure is applied to real data examples taken from the materials science.